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Defects Of Properties In Mathematics: Quantitative Characterizations: 5
Author(s): Adrian I. Ban (Author), Sorin G. Gal (Author)
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication Date: 23 April 2002
- Language: English
- Print length: 364 pages
- ISBN-10: 9810249241
- ISBN-13: 9789810249243
Book Description
This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the “deviation from a (given) property”, called the “defect of a property”, in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics.Besides well-known “defects”, the book introduces and studies new ones, such as: measures of noncompactness for fuzzy sets; fuzzy and intuitionistic entropies; the defect of (sub, super)additivity; complementarity; monotonicity for set functions; the defect of convexity; monotonicity; differentiability for real functions; the defect of equality for inequalities; the defect of orthogonality for sets and defects of properties for linear operators in normed spaces; defects of properties (commutativity, associativity, etc.) for binary operations; defects of orthogonality and parallelness in Euclidean and non-Euclidean geometries; defects of integer, perfect, prime and amicable numbers; the defect of tautology in fuzzy logic.
Editorial Reviews
Review
.,.” a good handbook-like source in general mathematics …”
